We also mention that we need \(\tau \)  to be large, but it is independent of \(t\) . In other words, we do not require a more and more precise Newton direction approximation as the iteration proceeds. This is in contrast to the inexact scheme in [1]}, which controls the approximation error by the KKT residual and a stepsize related sequence \(\beta _t\)  (cf. (REF )). In other words, [1]} controls the inexactness more adaptively, while the approximation error also has to diminish to zero.
